Possible or impossible to import 3D-models with correct UV-mapping and texture into Blender?
It is most definitely possible. If the models are modeled well and exported correctly to one of the huge number of formats that Blender supports you should have no problems. .obj, .fbx and .3ds as well as .dea files are among the most popular formats used. They all support geometry and UV Maps well. 

The problem with materials is that they differ too much in different software using different render engines (see this answer for more detailed explanation: .fbx export why there are no materials or textures?) so you will need to recreate them and assign the image textures during this process. This is true for any software, not just exporting from 3ds Max to Blender. You would have similar problems exporting from 3ds Max to Maya or Cinema 4D or Houdini or any other software that you would use a different rendering engine in.  

Regarding the models being a big mess, from my experience I can say that this very common situation very often has nothing to do with the software you are trying to import the models to. They could just be exported with settings not suitable for your purposes, but it is also very common for models that originate in solid modelling or other CAD software to have a very untidy and messy geometry making it a nightmare to work with them. This issue cannot be solved by switching to 3ds Max or any other 3d package unfortunately. My recommendation would be to check carefully if this is not the case before investing your money, effort and time into switching to another 3d package.